In dynamic MRI applications, such as functional imaging, interventional imaging and cardiac imaging, there has long been a need in the art for methods and apparatus that provide high quality (e.g., high-resolution and signal-to-noise ratio) images. Increased spatio-temporal resolution in MRI can be achieved using parallel acquisition strategies, which simultaneously sample reduced k-space data using the information from multiple receivers to reconstruct full Field-Of-View (FOV) images. The folded image that would result from a conventional reconstruction is avoided by using spatial information from multiple coils. Some of these conventional methods, such the SMASH method, are described in the Background section of U.S. Pat. No. 6,680,610 by Kyriakos et al. for “Apparatus and method for parallel MR data acquisition and parallel image reconstruction from multiple receiver coil arrays for fast MRI”, the disclosure of which is hereby incorporated by reference herein.
The reconstruction of parallel MRI can be formulated as linear equations in the literature of Sodickson et al (“A generalized approach to parallel magnetic resonance imaging” Med Phys 2001; 28: 1629–43.), which must include a matrix inversion process to obtain an unfolded image from the reduced k-space data set. If the matrix is well conditioned, the inversion can be achieved with a minimal amplification of noise. While the encoding matrix can still be inverted even if it is nearly singular, in this ill-conditioned case, small noise perturbations in the measured data (aliased image) can produce large variations in the full FOV reconstruction. This effect causes noise amplifications in regions of the image where the encoding matrix is ill conditioned.
The restoration of full-FOV images requires the use of additional information such as the coil sensitivity maps provided by a low spatial resolution full FOV reference scan. In addition to being required to determine the coil sensitivity profile that becomes part of the linear equations to be inverted, the reference scan might also provide a-priori information useful for regularizing the inversion process. The benefits of incorporating prior information to reduce the noise level of reconstructed images were reported in the literature (King, K. SENSE image quality improvement using matrix regularization In: Proceedings of the 9th Annual Meeting of ISMRM, Glasgow, Scotland, 2001. 1771; Tsao, J., Pruessmann, K. Boesiger, P. Prior-information-enhanced dynamic imaging using single or multiple coils with k-t BLAST and k-t SENSE In: International Society for Magnetic Resonance in Medicine Tenth Scientific Meeting and Exhibition, Honolulu, Hi., USA, 2002. 2369; Lin, F.-H., Kwong, K. K., Chen, Y.-J., Belliveau, J. W. Wald, L. L. Reconstruction of sensitivity encoded images using regularization and discrete time wavelet transform estimates of the coil maps In: International Society for Magnetic Resonance in Medicine Tenth Scientific Meeting and Exhibition, Honolulu, Hi., USA, 2002. 2389). Nevertheless, no systematic approach has been described to estimate a regularization parameter for SENSE image reconstruction. And spatial distribution of noise arising from unfolding SENSE images has not been well characterized when regularization is employed.